Subspaces of Rn The notion of subspace is a generalization of the geometric examples of lines and planes passing through the origin. In the following definition, when we write uS , we say that u belongs to S or u is an element of S . Definition: A subset S of Rn is called a subspace of Rn if all of the following conditions hold: (S0) 0S , where 0 is the zero vector in Rn . (S1) If u,vS , then u vS . (S2) If uS and cR , then cuS . Some explanations for where this definition comes from can be found in the video Subspaces 1. So, if (S1) holds for a certain subset S of Rn but (S2) fails, then S Answer 1 Question 1 a subspace. Note: If property (S1) holds, we say that S is closed u